Incremental Strongly Connected Components with Predictions

2026-04-28

AI Summary

This work addresses the problem of incrementally maintaining strongly connected components (SCCs) in directed graphs with fixed vertices and dynamically inserted edges. It introduces, for the first time, an algorithmic framework with predictions to this setting. The proposed method integrates online algorithms, prediction-guided preprocessing, and dynamic graph data structures, leveraging possibly imperfect predictions of future edge insertions to precompute partial solutions that accelerate update operations. Theoretical analysis demonstrates that the algorithm approaches optimal performance when predictions are accurate and degrades gracefully as prediction error increases. Extensive experiments on real-world datasets confirm substantial improvements in runtime efficiency, aligning closely with the theoretical guarantees.

Abstract

Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the $n$ vertices of a graph are known a priori and the $m$ directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.

Problem

• incremental
• strongly connected components
• dynamic graph
• graph algorithms
• data structures

Innovation

• algorithms with predictions
• incremental strongly connected components
• learned data structures
• beyond-worst-case analysis
• graph streaming